Previous mathematical models of CTL responses assumed that CTL expansion required continuous antigenic stimulation. Recent experiments have shown, however, that a single encounter with antigen can send CTL into a program of proliferation and differentiation. Execution of the program does not require further antigenic stimulation, and leads to the generation of effector and memory CTL. The proposal aims to construct and analyze mathematical models which describe the process of programmed CTL proliferation, and to couple the modeling work with experimental studies through a specific collaboration. The basic mathematical model will be validated with data from VSV infected mice, and this will involve the measurement of crucial parameters. It will be compared how the programmed proliferation model differs from the continuous stimulation models which have been used so far. Are the results from the continuous stimulation models obsolete or do they remain robust? Why has programmed proliferation evolved? After this general analysis two specific aspects of CTL dynamics will be investigated in the context of programmed proliferation. These are the role of effector molecules (such as perform and IFN-g) for CTL dynamics, and the role of CD4 T cell help. The modeling work will be complemented by experiments with VSV and LCMV infected mice.